Overview of quantum noise suppression techniques Helge Müller-Ebhardt, Henning Rehbein, Kentaro Somiya, Roman Schnabel, Karsten Danzmann and Yanbei Chen Max-Planck-Institut für Gravitationsphysik (AEI) Institut für Gravitationsphysik, Leibniz Universität Hannover TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAA

Quantum measurement noise measurement noise = photon shot noise + radiation pressure noise free mass dynamics quantum measurement process no correlation in shot and back-action noise measurement frequency

Quantum measurement noise measurement noise = photon shot noise + radiation pressure noise free mass dynamics quantum measurement process use correlation in shot and back-action noise measurement frequency

balanced homodyne detection QND techniques scheme benefit frequency band balanced homodyne detection pushes quantum noise down to shot noise level in radiation pressure dominated regime variational output overall frequencies squeezed input reduces quantum noise by the squeezing factor signal recycling increases sensitivity around resonances speed meter quantum noise parallel to standard quantum limit transducer at low frequencies double carrier at low frequencies and around resonances 4

QND techniques balanced homodyne detection at frequency-independent quadrature angle variational output with frequency-dependent quadrature angle [Kimble et al, 2001]

balanced homodyne detection QND techniques scheme benefit frequency band balanced homodyne detection pushes quantum noise down to shot noise level in radiation pressure dominated regime variational output overall frequencies squeezed input reduces quantum noise by the squeezing factor signal recycling increases sensitivity around resonances speed meter quantum noise parallel to standard quantum limit transducer at low frequencies double carrier at low frequencies and around resonances 6

QND techniques 10 dB squeezed input at frequency-independent quadrature angle 10 dB squeezed input with frequency-dependent quadrature angle [Kimble et al, 2001]

balanced homodyne detection QND techniques scheme benefit frequency band balanced homodyne detection pushes quantum noise down to shot noise level in radiation pressure dominated regime variational output overall frequencies squeezed input reduces quantum noise by the squeezing factor signal recycling increases sensitivity around resonances speed meter quantum noise parallel to standard quantum limit transducer at low frequencies double carrier at low frequencies and around resonances

Signal-recycled Michelson interferometer signal-recycling mirror at the dark output port → signal becomes amplified due to an increasing interaction time [Meers, 1988] detuned signal-recycling cavity → optical spring produces additional resonance [Buonanno & Chen, 2001 – 2003]

Optical spring effect a cavity which is detuned from the carrier's frequency makes the power inside the cavity dependent on the motion of the mirror

Optical spring effect a cavity which is detuned from the carrier's frequency makes the power inside the cavity dependent on the motion of the mirror damping anti-damping optical power lags behind the cavity motion → complex spring constant → system becomes unstable possible solution: stable double optical spring

Speed meter idea measure position difference after time delay → measure speed [Braginsky & Khalili, 1990] conserved momentum usually proportional to speed → real QND? no: because the coupling to speed changes conserved momentum [Khalili, 2002]

Speed meter realization two different optical realizations Michelson interferometer Sagnac interferometer [Purdue, 2002] [Chen, 2003]

Optical inertia effect a speed meter which is detuned from the carrier's frequency makes the fluctuating radiation-pressure force dependent on the acceleration of the mirror dynamical mass is modified

Signal-recycled Sagnac interferometer signal-recycling mirror at the dark output port - two optical resonances degenerated resonance case → speed meter bandwidth important factor

Signal-recycled Sagnac interferometer optimize quantum noise in vicinity of standard classical noise budget AdvLIGO-scale parameters fixed 40 kg mirrors 4 km arms 800 kW power optimization parameters sr detuning sr bandwidth arm cavity bandwidth (250 Hz) → finesse (150) improves AdvLIGO by 45 % in the event rate

Signal-recycled Sagnac interferometer optimize quantum noise in vicinity of future classical noise budget AdvLIGO-scale parameters fixed 40 kg mirrors 4 km arms 800 kW power optimization parameters sr detuning sr bandwidth arm cavity bandwidth (125 Hz) → finesse (300) improves Michelson by 230 % in the event rate

Transducer idea radiation pressure force can transduce motion between front and end mirror of a detuned cavity SQL of a local meter optical bar detector [Braginsky, Gorodetsky & Khalili, 1997]

Position meter transducer infinite optical inertia rigid optical spring zero optical inertia every position meter transducer becomes an optical bar at low frequencies SQL beating narrowband SQL beating

Speed meter transducer infinite optical inertia zero optical inertia speed meter transducer is more flexible at low frequencies

Local readout scheme second carrier senses motion of input mirrors both outputs are optimally filtered